SOLUTION: I have having problems with solving the following. If anyone can provide me with the steps it would be appreciated. The measurement of land area assumes that the land is horizo

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Question 144075: I have having problems with solving the following. If anyone can provide me with the steps it would be appreciated.
The measurement of land area assumes that the land is horizontal. What is the actual area of a 4.38 ha field if it is on a 15% slope.
Thanks, much appreciated.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Assuming the field is a square and has area = 4.58 on the horizontal,
it has a side of sqrt(4.58) = 2.1401..
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The 15% slope has a gradiant of 0.15*90 degrees = 13.5 degrees
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The horizontal side projects to a hypotenuse of a right triangle
with an angle of 13.5 degrees adjacent to the 2.1401.. base.
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The length of that projected hypotenuse is 2.1401../cos(13.5)
= 2.2009..
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Therefore the horizontal square projects to a quadrilateral with area
= 2.2009*2.1401 = 4.71012 ha
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Cheers,
Stan H.